Graph Theory Basics

Graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (or nodes) and edges (or lines). The nodes are the points and the edges are the lines connecting them.

Key Concepts

• Vertices: The individual points in a graph.
• Edges: The lines connecting vertices.
• Degree: The number of edges connected to a vertex.
• Connected Graph: A graph where there is a path between any two vertices.
• Directed Graph: A graph where edges have a direction.
• Weighted Graph: A graph where each edge has a weight or value associated with it.

Types of Graphs

• Simple Graph: A graph without loops or multiple edges between the same pair of vertices.
• Directed Graph: A graph where edges have a direction.
• Weighted Graph: A graph where each edge has a weight or value associated with it.

Applications

Graph theory has many applications in various fields such as computer science, operations research, and social sciences.

• Computer Science: Graphs are used to model networks such as social networks, computer networks, and the internet.
• Operations Research: Graphs are used to model and solve optimization problems.
• Social Sciences: Graphs are used to model social networks and relationships.

For more information on graph theory, you can visit our Graph Theory Deep Dive.

Example

Here's a simple graph representation:

    A
   / \
  B   C
   \ /
    D

In this graph, A, B, C, and D are vertices and the lines are edges.

Graph Example